Why a number to the zero power is equal one?

Answer 1

What is (53 / 5)? 125 / 5 = 25 = 5²

What is (5² / 5)? 25 / 5 = 5 = 51

What is (51 / 5)? 5 / 5 = 1 = 50

The above is the conventional answer. Thus making the actual answer "for purely conventional reasons only", for there is no actual logic to it. Else you could continue it and have:

What is (50 / 5)? 1/ 5 = .2 = 5-1 and you certainly never see anyone claim that 5-1 is equal to .2, do you?

Also consider:

What is 5²? Counting to five, five times - or 25.

What is 51? Counting to five just the once - or 5.

What is 50? Counting to five not at all - or 0.

See? The same steadily downward progression as in the first example. What does that mean? It means mathematics is a matter of convention, and those who do it most have simply decided it one way. They could have as easily decided it another way.